the possession of his cousin, Robert Smith, who bequeathed them to Edward Howkins, who in his turn bequeathed them, in 1779, to the College, where they have since remained. By order of the College they, together with drafts of the corresponding letters from Cotes to Newton and various other Newtonian papers, were printed in 1851, under the care of Dr. Edleston.

This collection also contains the four letters of 1692 and 1693 from Newton to Bentley, which were given by Bentley's nephew and executor to Richard Cumberland, who published them in 1756, and subsequently presented them to the College. From the same source is derived Newton's note on a course of mathematical reading which would give that preliminary knowledge of the subject necessary for the comprehension of the Principia.

The letter of Nov. 28, 1679, from Newton to Hooke, and the memoranda of Hooke on the controversy concerning the origin of the law of inverse squares, were recently purchased by the College, and are printed below for the first time.

(iv) The Macclesfield Collection at Sherborn Castle contains the greater part of the library formed by William Jones, which, besides his own correspondence, included the libraries and papers of Collins, Oughtred, and others. This came into the possession of Lord Macclesfield on Jones's death in 1749. The letters in this collection were published by Rigaud under the title, Correspondence of Scientific Men of the seventeenth century in the collection of the Earl of Macclesfield, Oxford, 1841, and a much-needed table of contents and index were issued in 1862. This book contains more than fifty letters from Newton himself, besides others with reference to his works. It would seem that the mathematical manuscripts in the collection (other than the letters) have not been catalogued or even carefully examined*. Rigaud, who saw them, says they "contain a "number of Newton's own MSS.," and it is likely that, but

* De Morgan in the Athenaeum, Oct. 18, 1862, p. 491, col. 1.

for Rigaud's premature death, he would have read them and published the results. Until the whole of this collection has been examined by some competent mathematician we cannot be sure that we have all the available data before us, but it would seem probable that the bulk of the documents in it are not directly connected with the history of the Principia.

Besides the four collections mentioned above there are letters from Newton in many public libraries, notably in the British Museum and in Corpus Christi College, Oxford. To a few of these letters I allude below, but most of them are on matters unconnected with the Principia.

6

CHAPTER II.

INVESTIGATIONS IN 1666.

Ir was in the year 1666 that Newton began to investigate the question of gravitation. He had taken the degree of B.A. in 1665, and, having thus completed the earlier part of his University course, he had leisure to pursue in his own way such studies as he pleased. Owing to the prevalence of the plague at Cambridge, he lived for a considerable part of the years 1665 and 1666 at his home in Lincolnshire, and it was there that the investigations described in this chapter were made.

The question of gravitation was one of the problems of the time, hence it was natural that he should consider it. It is, however, probable that at this period his enquiries on the subject were but of a slight character, and would have passed almost unnoticed had they not proved the earliest steps to his later discoveries.

His conclusions were not published, nor, as far as we know, are they contained in any manuscript now extant; but the following authorities enable us to form a general idea of their character and extent.

(i) First, there are allusions to the subject in letters from Newton, dated June 20, 1686, and July 14, 1686, which are printed below (pp. 156-162, 165).

(ii) Secondly, I may refer to the Portsmouth draft memorandum*, which he wrote some years later-perhaps about

* Portsmouth Collection, section 1. division xi. number 41.

1714. The original is cancelled, and hence it is not indisputable evidence; but it is believed that, except for certain dates in the paragraph next below, it is substantially correct. This draft is as follows:

I found the Method [of fluxions] by degrees in the years 1665 and 1666. In the beginning of the year 1665 I found the method of approximating Series and the Rule for reducing any dignity of any Binomial into such a series. The same year in May I found the method of tangents of Gregory and Slusius, and in November had the direct method of fluxions, and the next year in January had the Theory of colours, and in May following I had entrance into ye inverse method of fluxions. And the same year I began to think of gravity extending to ye orb of the Moon, and having found out how to estimate the force with wch [a] globe revolving within a sphere presses the surface of the sphere, from Kepler's Rule of the periodical times of the Planets being in a sesquialterate proportion of their distances from the centers of their Orbs I deduced that the forces wch keep the Planets in their Orbs must [be] reciprocally as the squares of their distances from the centers about wch they revolve: and thereby compared the force requisite to keep the Moon in her Orb with the force of gravity at the surface of the earth, and found them answer pretty nearly. All this was in the two plague years of 1665 and 1666, for in those days I was in the prime of my age for invention, and minded Mathematicks and Philosophy more than at any time since. What Mr. Hugens has published since about centrifugal forces I suppose he had before me. At length in the winter between the years 1676 and 1677 [probably this should be 1679 and 1680] I found the Proposition that by a centrifugal force reciprocally as the square of the distance a Planet must revolve in an Ellipsis about the center of the force placed in the lower umbilicus of the Ellipsis and with a radius drawn to that center describe areas proportional to the times. And in the winter between the years 1683 and 1684 [this should be the winter between 1684 and 1685] this Proposition with the Demonstration was entered in the Register book of the R. Society.

And on the next page, Newton continues:

By this Method [of fluxions] I invented the Demonstration of Kepler's Proposition in the year 1679, and almost all the rest of the Difficulter Propositions of the Book of Principles in the years 1681, 1685, and part of the year 1686.

(iii) Thirdly, the subject is mentioned by Whiston in hist autobiography, and he says that he obtained his information from Newton's conversations soon after 1694. The paragraphs referring to it are as follows*:

I proceed now in my own history. After I had taken Holy Orders, I returned to the College, and went on with my own Studies there, particularly the Mathematicks, and the Cartesian Philosophy; which was alone in Vogue with us at that Time. But it was not long before I, with immense Pains, but no Assistance, set myself with the utmost Zeal to the Study of Sir Isaac Newton's wonderful Discoveries in his Philosophiae Naturalis Principia Mathematica, one or two of which Lectures I had heard him read in the publick Schools, though I understood them not at all at that Time. We at Cambridge, poor Wretches, were ignominiously studying the fictitious Hypotheses of the Cartesian, which Sir Isaac Newton had also himself done formerly, as I have heard him say. What the Occasion of Sir Isaac Newton's leaving the Cartesian Philosophy, and of discovering his amazing Theory of Gravity was, I have heard him long ago, soon after my first Acquaintance with him, which was 1694, thus relate, and of which Dr. Pemberton gives the like Account, and somewhat more fully, in the Preface to his Explication of his Philosophy: It was this. An Inclination came into Sir Isaac's Mind to try, whether the same Power did not keep the Moon in her Orbit, notwithstanding her projectile Velocity, which he knew always tended to go along a strait Line the Tangent of that Orbit, which makes Stones and all heavy Bodies with us fall downward, and which we call Gravity? Taking this Postulatum, which had been thought of before, that such Power might decrease, in a duplicate Proportion of the Distances from the Earth's Center. Upon Sir Isaac's first Trial, when he took a Degree of a great Circle on the Earth's Surface, whence a Degree at the Distance of the Moon was to be determined also, to be 60 measured Miles only, according to the gross Measures then in Use. He was, in some Degree, disappointed, and the Power that restrained the Moon in her Orbit, measured by the versed Sines of that Orbit, appeared not to be quite the same that was to be expected, had it been the Power of Gravity alone, by which the Moon was there influenc'd. Upon this Disappointment, which made Sir Isaac suspect that this Power was partly that of Gravity, and partly that of Cartesius's Vortices, he threw aside the Paper of his

* Memoirs of the Life of Mr. William Whiston by himself, London, 1749, vol. i. pp. 35-38.